In a few months a certain game will be released on DSiWare. There's word it will also be released in the 3DS shop. Say that this is indeed the case and say it will have Download Play, would a regular DS be able to connect?

yep!
I have a DSiWare game called Pop Island/Paperfield. It's DSiWare, but any kind of ds system can download a demo version. you can even play multiplayer between DS systems with the full version and DS systems with the temporary demo! It's a rare example though.

Yeah, I already thought DS to DSi with DSiWare game wouldn't be a problem, but what if it is also released in the 3DS shop and you're trying to connect to that 3DS's version of the game? Would there then be compatibility? Or would the 3DS version of a DSiWare game be different in a sense where a regular Nintendo DS wouldn't be able to connect anymore? As the thing is, we have 0 DSi's here, 1 3DS and 2 regular DS's (it's not even said the game will have Download Play though, but considering its nature it would make sense).